Problem: Simplify; express your answer in exponential form. Assume $q\neq 0, p\neq 0$. $\dfrac{{(q^{-4})^{5}}}{{q^{-1}p^{-3}}}$
Solution: To start, try working on the numerator and the denominator independently. In the numerator, we have ${q^{-4}}$ to the exponent ${5}$ . Now ${-4 \times 5 = -20}$ , so ${(q^{-4})^{5} = q^{-20}}$ In the denominator, we can use the distributive property of exponents. ${q^{-1}p^{-3} = q^{-1}p^{-3}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(q^{-4})^{5}}}{{q^{-1}p^{-3}}} = \dfrac{{q^{-20}}}{{q^{-1}p^{-3}}}$ Break up the equation by variable and simplify. $\dfrac{{q^{-20}}}{{q^{-1}p^{-3}}} = \dfrac{{q^{-20}}}{{q^{-1}}} \cdot \dfrac{{1}}{{p^{-3}}} = q^{{-20} - {(-1)}} \cdot p^{- {(-3)}} = q^{-19}p^{3}$.